RECENT ADVANCES IN THE DESIGN AND CONSTRUCTION OF COMPOSITE FLOOR SYSTEMS

Transcription

1 PMayB5 16/8/214 1 RECENT ADVANCES IN THE DESIGN AND CONSTRUCTION OF COMPOSITE FLOOR SYSTEMS K F Chung and A J Wang The Hong Kong Polytechnic University, Hong Kong SAR, China. ABSTRACT This paper reviews the latest design developments on composite floor and beam systems fully integrated with building services. A number of composite floor systems developed specifically for integration of building services in commercial buildings are presented, namely, composite beams with fabricated I-sections with tapered webs, composite trusses, composite slim floor systems, and composite beams with perforated symmetric and asymmetric I-sections. Furthermore, recent advances in the analysis and design of steel and composite beams with large web openings are also presented while numerical tools specifically established for un-perforated and perforated composite beams with flexible shear connectors are also discussed. KEYWORDS Floor systems; Composite beams; Integration with building services; Web openings; development; Numerical models; flexible shear connectors. Design COMPOSITE CONSTRUCTION IN BUILDINGS Although many engineers tend to think that composite construction is a product of recent design and construction practice, it is actually began just prior to the start of the twentieth century. While many countries have their own stories to tell about composite construction, the first composite construction with design approval appeared in the year of 1894 when a bridge and a building were constructed in the USA, namely, the Rock Rapids Bridge in Rock Rapids, Iowa, and the Methodist Building in Pittsburgh. A hundred years on and more and more engineers capitalize the many advantages offered by the two most commonly used constructional materials, concrete and steel, to build stiff and strong structures with speed and economy. The structural system of a composite beam is essentially a T beam with a thin wide concrete flange connected with a steel section, as shown in Figure 1. The concrete flange is in compression and the steel section is largely in tension. The forces between the two materials are transferred by shear connectors, usually headed studs or other connectors which are welded or shot-fired to the steel

2 PMayB5 16/8/214 2 section and embedded in the concrete slab. The benefits of composite action are increased strength and stiffness with 1.5 to 2.5 times of moment resistance and flexural rigidity of the steel section, leading to considerable economy in the size of the steel beam used. Composite beams are often unpropped during construction, and the steel section is sized to support the self-weight of concrete slab and other construction loads before the concrete has gained adequate strength to develop composite action. D C D Concrete slab D P Shear connector Steel beam.45 f cu D R R c -D P C C R y C P yp y P P.N.A R S P.N.A p y P.N.A p y a) P.N.A in concrete b) P.N.A in steel flange c) P.N.A in steel web Figure 1 Stress blocks of composite beam The moment resistance of a composite beam is determined using plastic analysis principle as shown in Figure 1. It is assumed that the strains across the composite beam are sufficiently large that the stresses in the steel section are at their yield values throughout the section depth and that the concrete has reached its compressive strength. Depending on the relative size and strength between the concrete flange and the steel section, the plastic neutral axis may lie within the concrete flange, the top flange or the web of the steel section. The moment resistance of the composite beam may be evaluated accordingly. The design of composite beams with steel decking is covered in BS595: Part 3 [1], Eurocode 4 [2], AS2327 [3], and Hong Kong Steel Code [4]. Design handbooks for both steel and composite beams with profiled steel decking may also be found in the references [5-1]. COMPOSITE BEAMS AND FLOOR SYSTEMS INTEGRATED WITH BUILDING SERVICES Composite construction in commercial buildings has been well established in many countries. Hot rolled or fabricated steel frames together with pre-cast concrete or composite slabs provide an effective means of fast-track construction with column-free office spaces. Composite slabs are usually designed to span 3 to 4 m between supporting beams and their depth is typically 12 to 15 mm. This dictates the economic layout of the structural grid of a building. In general, there is always a need to incorporate a high degree of building services within the floor zones while at the same time to minimize the depth of floor zones in order to reduce the overall height of a building. The economics of modern buildings are such that a small increase in the cost of steel frames required to integrate structural members and building services has a proportionately much smaller effect on the overall cost of the buildings. Various design solutions are feasible, but there are two basic options: either the structural members and the building services are integrated within the same horizontal zone, or the structural zone is minimized so that the building services are passed beneath. The latter are often considered to be beneficial in offering greater flexibility of building use with high economy and versatile use over their entire life cycles.

3 PMayB5 16/8/214 3 Main structural features of these floor systems are presented in the following sections together with their typical applications. The typical spanning capacities of these floor systems are summarized in Table 1. For details on the design and use of each of the floor systems, refer to the list of references. Table 1 Summary of typical spans of composite floor and beam systems Span (m) Reinforced concrete flat slab 2 Reinforced concrete beam and slab 3 Post-tensiond concrete flat slab 4 Composite beam and slab 5 Composite fabricated I section with tapered web 6 Composite haunched beam 7 Composite truss 8 Composite stub girder 9 Composite parallel beam grillage system 1 Composite slim floor with deep slab 11 Composite beam with perforated I section 12 Composite castellated beam Composite Beams with Fabricated I-sections and Tapered Webs The use of fabricated I sections with tapered webs [11] is always regarded to be structurally effective where the beams are designed to provide the required moment and shear capacities at all points along the member lengths with minimum materials. As shown in Figure 2, the voids thus created adjacent to columns may be used for building services of small to medium sizes. Due to the use of non-prismatic members, it is difficult to locate the critical cross-sections under the action of combined moment and shear, and thus much design effort is required. In general, the cross-section dimensions of the flanges remain constant along the beam length while the depth of the webs increases according to the applied moments; vertical web stiffeners are often required at the change of cross-section. In practice, maximum efficiency is only likely to be achieved by the use of specialist design software where the dimensions of the flanges and the webs are selected for optimum structural performance. The economic advantages of fabricated I-sections are critically related to the refinement effort on the design process, and typically, they are most economic for spans of 12 to 2 m. All the steel plates are usually welded in an automatic single-sided submerged arc process.

4 PMayB5 16/8/214 4 Composite Trusses with Tee and Angle Sections Composite trusses [12] are commonly used in multi-storey buildings for long span floors of 12 to 25 m. The trusses are usually designed to occupy the full depth of the floor zone with a standard 'Warren trusses' so that building services may pass through the voids created between the chords and the diagonals as shown in Figure 3. Furthermore, a central Vierendeel panel without diagonals is often introduced to provide large void for building services at mid-span. The trusses are usually fabricated from tee-sections as top and bottom chords, and angle sections as diagonals. In long span applications, composite action provides only a moderate increase in strength but a significant increase in flexural rigidity against deflection. In general, the cost of fabrication and fire protection may be high in relation to the material cost, but they are very popular in practice as they are structurally efficient and provide a high degree of routing flexibility for building services. Composite Slim Floor Systems Slim floor systems are developed in the 199's in the U.K. where concrete slabs are placed within the depth of primary steel beams to provide floor systems with a minimum constructional depth as shown in Figure 4. I general, no secondary beams are needed while ties are provided between primary beams at regular intervals wherever necessary. Universal column sections with welded bottom plates are first introduced, and later, hot rolled asymmetric steel sections with unequal flanges are specifically developed for this form of construction [13]. Both precast concrete slabs and composite slabs with deep profiled steel decking may be used. Typical beam spans range from 5 to 7.5 m with an overall floor depth of 32 mm. Circular web openings may be provided in the floor systems using composite slabs with deep profiled steel decking in order to provide passage of building services. As the top flange, the web and also part of the bottom flange of the steel beams are encased within the concrete slabs, the inherent fire resistance of the floor systems is very high. In general, a fire resistance period of 6 min. is readily achieved without fire protection. For a fire resistance period of 9 min., only nominal fire protection is needed at the exposed bottom flanges of the steel beams. Although the slim floor systems may not be as structurally efficient as other conventional floor systems due to small structural depths, the overall construction cost is yet considered to be competitive as no or little fire protection is needed. COMPOSITE BEAMS WITH PERFORATED I-SECTIONS Over the past few decades, the structural behaviour of beams with web openings was a popular research topic, and numerous research projects were executed and reported including experimental investigations, finite element studies and also development of design rules. In general, rectangular web openings were examined extensively while other opening shapes such as hexagonal and circular openings have also been studied. A number of national and international design recommendations [7, 9, 14-17] are available to design both steel and composite beams with rectangular and hexagonal web openings of medium sizes.

5 PMayB5 16/8/214 5 Composite Beams with Single Web Openings In this method of construction, large individual openings are formed in the webs of steel beams to provide passage of building services at specific locations as shown in Figure 5. The presence of web openings may have a severe penalty on the load carrying capacities of floor beams, depending on the shapes, the sizes, and the locations of the web openings. The presence of web openings in steel beams introduces three different modes of failure at the perforated sections: Shear failure due to reduced shear capacity Flexural failure due to reduced moment capacity 'Vierendeel' mechanism due to the formation of four plastic hinges in the tee-sections above and below the web openings under the Vierendeel action. The depth of the steel beam is selected so that sufficiently large, usually rectangular or circular openings can be cut into the web. In general, the opening depth should not be larger than two-third of the depth of the steel beams while the opening length should not be larger than 1.5 times the beam depth. Horizontal reinforcements may be welded above and below the opening whenever necessary. The best location of the openings is normally in the low shear zone of the beams. Specific design rules against Vierendeel mechanism are necessary, and interaction between coexisting axial force, shear force and bending moment in assessing section capacities is important. A number of design methods with semi-empirical expressions are available in the literature. Composite Beams with Multiple Web Openings In this method of construction, castellated steel beams with hexagonal web openings are fabricated from universal beams with profile cutting and welding so that the overall beam depth of the perforated sections was increased by 5% for enhanced structural performance against bending, as shown in Figure 6. Castellated beams with large circular openings are also fabricated with advanced profile cutting. In additional to those failure modes associated with steel beams with single web openings, buckling of web posts may be critical in castellated beams when the openings are closely spaced. Moreover, additional deflection due to the presence of web openings should also be considered. In typical applications, the opening depth is two-third of the overall section depth of the parent section while the maximum length to depth ratio of the openings is about.83. The length of the tee sections above and below the opening is only about a quarter of the opening depth, producing a very efficient perforated section against Viereendel mechanism. No reinforcements are normally provided. Castellated beams are effectively used in highly serviced buildings and they are also popular in exposed roof and floor systems for aesthetic reasons. In composite castellated beams, composite action does not significantly increase the strength of the beams but their flexural rigidity stiffness is enhanced enormously. They have limited shear capacity and are best used as long span secondary beams or where loads are relatively low.

6 PMayB5 16/8/214 6 Shear connector Reinforcement slab with Composite slab with profiled steel decking profiled steel decking Secondary beams Figure 2 3. Fabricated beam with tapered web Composite beam with fabricated I section and tapered web Shear connector Shear connector Reinforcement Reinforcement Composite slab with profiled steel decking Composite slab with profiled steel decking Figure 3 5. Truss Composite truss with tee and angle sections No shear connector is needed is needed Reinforcement Reinforcement Composite slab with deep profiled steel decking Composite slab with deep profiled steel decking Main slab Main reinforcement slab reinforcement Primary beam Figure 4 8. Slim floor system Composite slim floor system

7 PMayB5 16/8/214 7 Shear Shear connector connector Reinforcement Composite slab with with profiled steel decking Reinforcement Reinforcement Primary beam or or secondary beam secondary beam Figure 5 9. Composite Beam beam with with single web web openings openings Shear Shear connector connector Reinforcement Composite slab with profiled profiled steel steel decking Primary beam or or secondary beam secondary beam Figure 6 1. Fabricated castellated beam with multiple web openings Composite beam with multiple web openings Design Methods for Beams with Rectangular Web Openings There are a number of design recommendations [9, 14, 16, 17] available in the literature for both steel beams and composite beams with rectangular web openings. In general, the design rules for both the shear and the moment capacities of perforated sections are relatively simple and similar. However, there are a number of different methods in allowing the effect of co-existing axial and shear forces in assessing the moment capacities of tee sections. The design rules are complicated and they differ significantly among each other, depending on the design methodology adopted, and also the accuracy and the calculation efforts involved. An overall review on the design recommendations shows that in general, there are two design approaches in assessing the structural behaviour of steel beams with rectangular web openings:

8 PMayB5 16/8/214 8 Tee section approach In this approach, the perforated section is considered to be built up of two tee sections which are separated by a distance according to the height of the web opening, and all the global actions are re-presented as local forces and moments. The structural adequacy of the steel beams depends on the section capacities of the tee sections under co-existing axial and shear forces, and local moments. In general, the design procedures are usually complicated, and the calculation effort is considerable. The accuracy of the design depends on the accuracy of a number of design rules against respective failure modes. Due to the complexity of the problems, approximate design expressions are often presented to reduce calculation effort, leading to conservative results. Perforated section approach In this approach, the perforated section is the critical section to be considered in design, and the structural adequacy of the steel beams depends on the section capacities of the perforated sections under co-existing shear force and bending moment due to global actions. Simple shear moment interaction curves are often used. However, as no specific check against the Vierendeel mechanism is considered, the design procedures are generally simple but very conservative results may be obtained. Design Methods for Steel Beams with Web Openings of Various Shapes and Sizes In order to provide guidance to engineers to design perforated steel beams for full integration with building services, it is highly desirable to develop a simple design method applicable to perforated sections of various shapes and sizes. A comprehensive and systematic parametric study [18] on steel beams with web openings of various shapes and sizes using finite element technique is reported in the literature, and the primary structural characteristics of those steel beams are examined in details. In the study, a number of common opening shapes was covered, including circular, hexagonal, octagonal, square, rectangular and elongated circular openings while the opening depth ranged from 5%, 67% to 75% of the section height of the steel beams. The finite element model is illustrated in Figure 7. It is found that all these steel beams behave similarly to each other in terms of deformed shapes under a wide range of applied moments and shear forces. Moreover, the yield patterns of those perforated sections at failure are also similar to each other, and in general, plastic hinges are always formed at both ends of the tee-sections above and below the web openings. As shown in Figure 8, comparison on the global moment-shear interaction curves of those steel beams with web openings of various shapes shows that they are also similar to each other in shape. The failure modes are common to all beams, namely, i) shear failure, ii) flexural failure, and iii) Vierendeel mechanism, as shown in Figure 9. Furthermore, it is shown that for all web openings of various shapes and sizes considered in the study, the most important parameter in assessing the structural behaviour of the perforated sections is the critical opening length, c, which controls the magnitude of local Vierendeel moments acting on the tee-sections. Consequently, it is possible to derive empirical moment-shear interaction curves to assess the load capacities of all these steel beams using generalized design rules.

9 Applied Shear Force V o,sd (kn) PMayB5 16/8/214 9 V h Plane of symmetry stress s LMS M V o,sd o,sd V x ( 1) V HMS V s Yield strength = 275N/mm 2 E = 2kN/mm 2 x Plane of symmetry strain Assumed stress-strain model Figure 7 Finite element model of a perforated section for parametric study A1 B1 C1 B2 A2 c-hexagon Circle Regular Octagon Regular Hexagon Square Elongated circle 2do Rectangle 2:1 Elongated circle 3do Figure 8 D 1 E 1 G 1 F 1 H1 H2 F2 G2 E2 H3 F3 D Applied Moment M o,sd (knm) Shear-moment interaction curves for perforated sections (UB457x152x52 S275 with d o /h =.75) C2 G3 E3 D3 C3 B3 A3 4

10 PMayB5 16/8/214 1 A2 B2 C2 D2 E2 F2 G2 H2 Figure 9 Deformation at failure for openings under large global shear and moment (UB S275 and d o /h=.75)

11 PMayB5 16/8/ Generalized moment-shear interaction curve In general, an interaction curve with an elliptical expression may be used to allow for interaction between moment and shear force in solid rectangular plates: or where v m where V o,sd, M o,sd V o,rd, M o,rd v m 2 + v 2 = 1 (1a) 2 1 m (1b) is the shear utilization ratio; Vo,Sd = ; (1c) V o,rd is the moment utilization ratio; Mo,Sd =. (1d) M o,rd are the applied shear forces and moments of the perforated section, respectively; are the shear force and moment capacities of the perforated section, respectively. However, for perforated sections, this interaction curve should be modified to allow for the presence of Vierendeel mechanism [19]. In general, for perforated sections under zero global moment, the shear utilization ratios are reduced from unity to the coupled shear capacity ratios, v. In the presence of global moments, the shear utilization ratios of the perforated sections will diminish gradually, depending on the magnitudes of the global moments. After careful calibration with the moment-shear interaction curves obtained from the finite element investigation, a generalized moment-shear interaction curve is recommended as follows: For For v v 3 m 1 v v ( v 2 ) v m (2a) (2b) where m where M,o,Rd,Vi is the coupled moment capacity ratio; Mo,Rd,Vi = ; (2c) M o,rd is the coupled moment capacity of the perforated section against Vierendeel mechanism. For analysis, the shear utilization ratio, v, and the moment coupled moment capacity ratio, m, are given by:

12 PMayB5 16/8/ For 2 v 2 v v 1 m v or 3 m 1 v (3a) v 2 For v v v 1 m v or m v 1 v (3b) In all cases, the shear utilization ratio, v, should not exceed the coupled shear capacity ratio, v. Figure 1 plots the proposed moment-shear interaction curves for web openings with various shapes and sizes, and they are considered to be applicable to steel beams with practical section sizes. It is important to note that, based on the three ratios, namely, the shear utilization ratio, v, the moment utilization ratio, m, and the coupled shear capacity ratio, v, the load carrying capacities of steel beams with web openings of various shapes and sizes may be obtained readily through the proposed moment-shear interaction curve. Design Methods of Composite Beams with Web Openings In order to provide design guidance to structural engineers in the U.K, a design method [14] was developed and formulated in accordance with BS595 for composite beams with large rectangular web openings. The design method was then calibrated against the test results of full-scale composite beams in 1992 [2]. With the release of Eurocode 4, the design method is re-presented in the format of application rules to Eurocode 4 for detailed design of composite beams with large web openings [21]. Moreover, in order to provide advice to engineers at the scheme design stage, general information on sizing of openings is also presented as a function of the utilization of the shear and the moment resistances of composite beams. The effect of these openings on deflection is estimated by a simple factor, which is dependent on the size and the location of the openings. Typical design tables for composite beams with large rectangular openings are also available. Design rules for other forms of construction such as circular openings and notched beams are also provided together with general detailing rules in the literature [21]. More recently, a unified design approach for both steel and composite beams with large rectangular web openings is proposed [22] which is based on plastic design methods and formulated in accordance with analytical structural design principles. In order to verify the proposed design rules, a finite element model using the general purpose finite element package ABAQUS is established to assess the structural behaviour of simply supported composite beams with perforated I-sections. Since the principal mode of failure involves only in-plane deformation, two-dimensional finite element models are adopted for simplicity. The test results of two simply supported composite beams with rectangular web openings are adopted to calibrate the finite element model. It is demonstrated that the proposed design method is able to predict the ultimate loads of composite beams with rectangular web openings against Vierendeel mechanism satisfactorily.

13 Shear ratio Shear ratio Shear ratio Shear ratio PMayB5 16/8/ C-hexagon.9 Circle do =.75h do =.67h do =.5h Regular Octagon 1..9 Regular Hexagon Moment ratio.9 do =.75h do =.67h Square.8 do =.5h Moment ratio Rectangle.9 Elongated circle 2d o.9 Elongated circle 3d o Moment ratio Moment ratio Figure 1 Proposed moment-shear interaction curves

14 PMayB5 16/8/ NUMERICAL MODELS ON CONTINUOUS COMPOSITE BEAMS WITH FLEXIBLE SHEAR CONNECTORS In order to establish an alternate design and analysis tool to assess the general structural behaviour of composite beams, the finite element model for simply supported composite beams [23] is extended to study continuous composite beams with either un-perforated and perforated I-sections. Main features of the finite element models [23] are : Iso-parametric four-node two-dimensional plane stress elements, CPS4R, are used to model both the concrete slabs and the steel beams. It should be noted that according to the geometry of the composite beams, the thicknesses of the plane stress elements are assigned to be equal to the widths of the concrete flanges, the widths of the flanges of the steel beams, and also the thicknesses of the webs of the steel beams. A bi-linear stress-strain curve is adopted in the material model of steel. For concrete, a conservative non-linear stress-strain curve under uni-axial loading condition is adopted in the material model of concrete while concrete crushing is included through the use of the material option * CONCRETE [24,25]. Moreover, effective steel reinforcement is assumed to be provided in the concrete, in particular, in the hogging moment region near internal supports; hence, there is no cracking in the concrete slab. It should be noted that the tensile strength of the reinforced concrete is taken as 1% of its compressive strength, and it is assumed to be able to exhibit limited degrees of ductility. With both material and geometric non-linearities incorporated into the finite element models, large deformation in the critical sections of the continuous beams after yielding is predicted accurately to allow for load re-distribution within the beam members. It should be noted that the test results of a continuous composite beam with solid concrete slab reported by Gattesco [26] were selected from the literature to calibrate the finite element models, and the general test set-up and the dimensions of the composite beam of Beam CTB4 are shown in Figure 11 together with its finite element model. All the measured mechanical properties of the concrete slab and the steel beam are adopted in the finite element model. Load-slippage Curves of Shear Connectors In order to simulate composite action in a composite beam between the solid concrete slab and the steel beam, each shear connector at the steel concrete interface is modelled with a horizontal spring and a vertical spring for shear and axial deformation respectively. However, it should be noted that while 19 mm diameter headed shear studs were adopted in both tests, no information on the actual load-slippage curves of the shear connectors was available. In order to determine the shear resistances of 19 mm diameter headed shear studs, reference is made to various design recommendations on the characteristic shear resistances of the shear connectors. In the present study, the following three shear connectors with different bi-linear deformation characteristics are adopted as follows:

15 PMayB5 16/8/ ) Shear connector P-R-72 Elasto-plastic with infinite stiffness and P s = 72 kn 2) Shear connector P-1-72 Elasto-plastic with K s = 1 kn/m and P s = 72 kn 3) Shear connector P-5-72 Elasto-plastic with K s = 5 kn/m and P s = 72 kn where P s, K s are the longitudinal shear resistance and the longitudinal shear stiffness of the shear connector, respectively. Alternatively, the load-slippage curve of the headed shear stud may be represented analytically [27] as follows: F s = P s ( 1 e -s ) α (4) where F s is the longitudinal shear force developed in the shear stud at a slippage of s (in mm); α is a non-dimensional parameter with its value between.5 and 1.5; and is a parameter with a unit of mm -1 ; its value is typically between.5 and 2.. Hence, the following shear connector with non-linear deformation characteristics is also adopted: 4) Shear connector N-72 Non-linear with α =.8 and = 2. in Eqn. (3), and P s = 72 kn It should be noted that these four shear connectors represent extreme and typical values found in composite beams with both solid concrete slabs and composite slabs with trapezoidal steel decks. It should be noted that the stiffness of the vertical spring of the shear connector, K v, is equal to that of the horizontal spring, K s. Moreover, the pull-out resistance of the shear connector, P v, is taken as half of its shear resistance, P s. After successful calibration against test data, the finite element model is modified to include a rectangular opening in the web near the internal support, as shown in Figure 12, in order to examine the structural behaviour of the continuous composite beam with perforated I-section, namely Beam CBT4-P. Moreover, the effects of shear connectors with different stiffnesses and resistances on the structural behaviour of un-perforated and perforated composite beams are examined thoroughly. Numerical Results Figure 13a) illustrates the deformed shape of the composite beam in Beam CTB4 at failure together with the stress distributions in the concrete slab and the steel beam. It is evident to see the twostage plastic hinge mechanism of the composite beam, and large local bending stresses are present at the critical cross-sections of the beam, as shown in Figure 13b). The load deflection curves predicted from the finite element models with shear connectors of different stiffnesses and resistances are plotted in the same graphs of the measured data, as shown in Figure 13c), for direct comparison with test data. It is shown that the predicted load deflection curves derived from the numerical studies compare very well with the experimental data. As a solid concrete slab is adopted in the composite beam, the load deflection curve of the finite element model with shear connector P-R-72 is found to follow closely with the test data. Moreover, the use of non-linear load-slippage curve in shear connector N-72 tends to give a load-deflection curve very close to that with shear connector P-1-72.

16 PMayB5 16/8/ A P/ A 45 HEA Section A-A (a)details of test specimen P/2 P/2 1 Δ Δ Ph (kn) P-R-72 P-1-72 N-72 three shear connectors three shear connectors 2 P-5-72 (b) Finite element mesh Figure 11: Double span composite beam with solid slab Beam CTB Δ h (mm) Notes: a) All dimensions are in mm. b) The cylinder strength of concrete is 38.4 N/mm 2. c) The mean yielding stress of steel is 236 N/mm 2. d) Three 19 mm headed shear studs are placed in each row. e) Every shear connector is modeled by one vertical and one horizontal spring.

17 PMayB5 16/8/ P/2 225 B 13 HEA B Section B-B (a)details of test specimen P/2 P/2 Δ Δ Ph (kn) P-R-72 P-1-72 N-72 three shear connectors three shear connectors 2 P-5-72 (c) Finite element mesh Δ h (mm) Notes: a) All dimensions are in mm. b) The cylinder strength of concrete is 38.4 N/mm 2. c) The mean yielding stress of steel is 236 N/mm 2. d) Three 19mm headed shear studs are placed in each row. e) Every shear connector is modeled by one vertical and one horizontal spring. Figure 12: Double span perforated composite beam with solid slab Beam CTB4P

18 Total load, P (kn) Total load, P (kn) Apllied load, P (kn) Total load, P (kn) PMayB5 16/8/ P/2 (a) Deformation shape Slab Tension Compression Direct stress p t -.25 p c -.5 p c -.75 p c -1. p c Steel beam Tension Compression Direct stress 1. p y.75 p y.5 p y.25 p y -.25 p y -.5 p y -.75 p y -1. p y 5 5 Near mid-span Near internal support (b) Direct stress distributions Limiting deflection at mid-span Δ l = 25 mm Test E-R E-R P-R-72 P-R-72 N-72 N-72 E-1 E-1 P-1-72 P-1-72 Test Test P-5-72 P Vertical Vertical deflection Deflection deflection at mid-span, at at mid-span, Δ (mm) Δ (mm) (c) Load-deflection curves Figure 13: Results of finite element modeling Beam CTB4

19 PMayB5 16/8/ Figure 14a) illustrates the deformed shape of the modified composite beam in Beam CTB4-P at failure together with the stress distributions in the concrete slab as well as the top composite and the bottom steel tee sections above and below the web opening. It is evident to see that the composite beam fails in the two-stage plastic hinge mechanism initiated with Vierendeel mechanism, and large local bending stresses are present at the critical cross-sections of the beam, as shown in Figure 14b). The load deflection curves predicted from the finite element models with shear connectors of different stiffnesses and resistances are plotted in the same graphs of the measured data, as shown in Figure 14c), for direct comparison. It is shown that the load deflection curves of the finite element model with shear connectors of different stiffnesses are similar in shape. In order to define the load carrying capacities of composite beams at large deformation, the load carrying capacity of the composite beam is assigned to be equal to the applied load where the maximum deflection reaches the smallest of: i) overall beam span over 9; ii) overall beam depth over 1; or iii) 25 mm. According to the proposed criterion, the load carrying capacity of the finite element model of Beam CTB4 with shear connector P-R-72 is found to be close to the test value. It should be noted that, contrary to the findings of the study on simply supported composite beams, the stiffnesses of shear connectors are found to be important in assessing the load carrying capacities of continuous composite beams, as shown in Figures 13c) and 14c) for Beams CTB4 and CTB4-P, respectively. Forces and slippages of shear connectors The longitudinal shear force, F s, and the vertical pull-out force, F v, of shear connectors with different stiffnesses and resistances for both Beams CTB4 and CTB4-P are plotted in Figure 15. It should be noted that the shear connector in the vicinity of the web opening in Beam CBT4-P is found to be highly stressed, in both the longitudinal and the vertical directions, when compared with that in Beam CBT4. Moreover, due to the presence of co-existing longitudinal shear and vertical pull-out forces in the shear connector in the close vicinity of the web opening, it is essential to check structural adequacy of the shear connector under combined shear and tension forces. The variations of slippages of shear connectors with different stiffnesses and resistances along the beam lengths are also presented in Figure 15. It should be noted that in Beam CBT4, the predicted maximum slippage occurs near the ends of the composite beams, as commonly envisaged, and the maximum end slippages are found to range from.25 to.8 mm, depending on the stiffnesses of the shear connectors. However, in Beam CBT4-P, there is also a significant slippage in the shear connector in the close vicinity of the web openings.

20 Total load, P (kn) Total load, Total P load, (kn) P (kn) Apllied load, P (kn) PMayB5 16/8/214 2 P/2 (a) Deformation shape Slab Tension Compression Direct stress p t -.25 p c -.5 p c -.75 p c -1. p c Steel beam Tension Compression Direct stress 1. p y.75 p y.5 p y.25 p y -.25 p y -.5 p y -.75 p y -1. p y 5 5 Near mid-span Near internal support (b) Direct stress distributions Limiting deflection at mid-span Δ l = 25 mm Test E-R E-R P-R-72 P-R-72 P-1-72 N-72 N-72 P-5-72 E-1 E-1 P-1-72 P-1-72 P-R-72 Test Test P-5-72 P-5-72P-N Vertical Vertical deflection Deflection deflection at mid-span, at at mid-span, Δ (mm) Δ (mm) (c) Load-deflection curves Figure 14: Results of finite element modeling Beam CTB4-P

21 Slippage, s (mm) Slippage, s (mm) Pull-out force, F v (kn) Pull-out force, F v (kn) Longitudinal force, F s (kn) Longitudinal force, F s (kn) 3 3 PMayB5 16/8/ P/2 = 212 kn P/2 = 19 kn 8 6 P-R-72 P-1-72 P-5-72 N P-R-72 P-1-72 P-5-72 N Distance away from left support (mm) Distance away from left support (mm) Distance away from left support (mm) Distance away from left support (mm) Distance away from left support (mm) Distance away from left support (mm) Beam CBT4 Beam CBT4P Figure 15: Internal force and slippage distributions of shear connectors

22 PMayB5 16/8/ CONCLUSIONS A review on composite floor and beam systems fully integrated with building services is presented, and main structural features, common design considerations and typical uses of these beams and floor systems are discussed. Moreover, a generalized design method for steel beams with web openings of different shapes and sizes is also presented when a recently proposed design method for composite beams with large rectangular web openings is described briefly. In order to establish an alternate design and analysis tool to assess the structural behaviour of composite beams with large rectangular web openings, a finite element model on two continuous composite beams is established and fully presented in this paper. Calibration on the model against test data is found to be satisfactory. It should be noted that the proposed finite element models are readily extended to cover many different design cases, such as composite beams with web openings of different sizes and shapes, composite beams with reinforced web openings, composite beams with asymmetric steel beams and eccentric web openings, and continuous perforated steel and composite beams. Through the provision of technical information on both the design of proven forms of construction and the recent advances in design development, engineers are encouraged to fully exploit the advantages offered by composite construction in modern commercial buildings with high specification on building services. References 1. British Standards Institution. BS595: Structural use of steelwork in building. Part 3 Section 3.1: Code of practice for design of composite beams. BSI, London, British Standards Institution. DD ENV Eurocode 4: Design of composite steel and concrete structures. Part 1.1: General rules and rules for buildings. BSI, London, Standards Australia. Composite Structures. Part 1: Simply supported beams. Australian Standard AS The Buildings Department of the Government of Hong Kong SAR (25). The Hong Kong Steel Code: Chapter 1: Composite Structures. 5. Chien EYL and Ritchie JK. Design and construction of composite floor systems. Canadian Institute of Steel Construction, Lawson RM. Design of composite slabs and beams with steel decking. The Steel Construction Institute, Johnson RP and Anderson D. Designers handbook to Eurocode 4: Part 1.1: Design of composite steel and concrete structures. Thomas Telford, London, Lawson RM and Chung KF. Composite beam design to Eurocode 4. The Steel Construction Institute, Oehlers DJ and Bradford MA. Composite steel and concrete structural members: Fundamental behaviour. Pergamon, Composite beam design handbook in accordance with AS , jointly published by the Australian Institute of Steel Construction and Standards Australia, SAA HB91, Owens GW. Design of fabricated composite beams in buildings. The Steel Construction Institute, Neal S and Johnson R. Design of composite trusses. The Steel Construction Institute, Lawson RM, Mullett DL and Rackham JW. Design of asymmetric slimflor beams using deep composite decking. The Steel Construction Institute, Lawson RM. Design for openings in the webs of composite beams. CIRIA Special Publication and SCI Publication 68, CIRIA / Steel Construction Institute, 1987.

23 PMayB5 16/8/ Ward JK. Design of composite and non-composite cellular beams. The Steel Construction Institute, Darwin D. Steel and composite beams with web openings. American Institute of Steel Construction, Steel Design Guide Series No. 2, Chicago, IL, USA, Redwood RG and Cho SH. Design of steel and composite beams with web openings. Journal of Constructional Steel Research, 1993, Vol. 25, pp Liu TCH and Chung KF. Steel beams with large web openings of various shapes: Finite element study. Journal of Constructional Steel Research, 23, Vol. 59, pp Chung KF and Liu TCH. Steel beams with large web openings of various shapes: Empirical design method. Journal of Constructional Steel Research, 23, Vol. 59, pp Lawson RM, Chung KF and Price AM. Tests on composite beams with large web openings to justify existing design methods. The Structural Engineer, 1992, Vol. 7, No. 1, pp Chung KF and Lawson RM. Simplified design of composite beams with large web openings to Eurocode 4. Journal of Constructional Steel Research, 21, Vol. 57, pp Chung KF, Ko CH and Wang AJ. Design of steel and composite beams with web openings Verification using finite element method. Steel and Composite Structures, 25, Vol. 5, pp Wang AJ and Chung KF. Numerical studies on perforated composite beams with flexible shear connectors. Journal of Constructional Steel Research (submitted for publication). 24. Baskar K, Shanmugam NE and Thevendran V. Finite-element analysis of steel-concrete composite plate girder. Journal of Structural Engineering, 22, Vol. 128, No. 9, pp Lam D and El-Lobody E. Behavior of headed stud shear connectors in composite beam. Journal of Structural Engineering, 25, Vol. 131, No. 1, pp Gattesco N. Analytical modelling of nonlinear ehaviour of composite beams with deformable connection. Journal of Constructional Steel Research, 1999, Vol. 52, pp Ollgaard JG, Slutter RG and Fisher JW. Shear strength of stud connectors in lightweight and normal weight concrete. AISC Engineering Journal, 1971, Col. 8, No. 2, pp55-64.